Related papers: Topological Data Analysis in Text Classification: …
Text classification, as the task consisting in assigning categories to textual instances, is a very common task in information science. Methods learning distributed representations of words, such as word embeddings, have become popular in…
With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…
The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…
This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…
Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity…
Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…
Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature…
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
Finance is heavily influenced by data-driven decision-making. Meanwhile, our ability to comprehend the full informational content of data sets remains impeded by the tools we apply in analysis, especially where the data is high-dimensional.…
We introduce second-order vector representations of words, induced from nearest neighborhood topological features in pre-trained contextual word embeddings. We then analyze the effects of using second-order embeddings as input features in…
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to…
Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…
A method of {\it topological grammars} is proposed for multidimensional data approximation. For data with complex topology we define a {\it principal cubic complex} of low dimension and given complexity that gives the best approximation for…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
Text classification is a fundamental problem in the field of natural language processing. Text classification mainly focuses on giving more importance to all the relevant features that help classify the textual data. Apart from these, the…
Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…
Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…